Hard Sphere Thermodynamic and Transport Properties

BULK-SLIT-HS: properties of the hard-sphere fluid in bulk and confined to a slit pore 
This page gives some results for hard-sphere fluids [1]

Methods: 
Event-driven molecular dynamics (MD) [1] and Transition-matrix Monte Carlo (TMMC) [2, 7-12].

Remarks: 

TMMC data is taken from Refs.[5,6].  Data for MD simulations was produced using N=4000 particles. All systems were equilibrated for 1000 reduced time units. Productions runs of time t>100,000 reduced time units were used. Self-diffusivities were calculated from the Einstein relation D_x=dx(t)^2, t->infinity, were dx(t)^2 is the mean square displacement in direction x. For the bulk self-diffusivity, all three directions where averaged together.  For the slit-pore self-diffusivity, only the periodic x and y directions (see schematic below) were averaged together. Mean-squared displacements were measured over times windows exceeding 5000 reduced units, using standard block averaging [1]. No less than 5 independent (different random seeds) were conducted at each state point.  This data was averaged to give the mean properties.  Errors were estimated by standard methods to yield the 95% confidence intervals.  That is, the error was take as T(n)*STD/sqrt(n), where n is the number of independent samples, T is the inverse student's t PDF at 95% level for n samples, and STD is the sample standard deviation of the independent samples.

 

Bulk properties:

sigma	particle diameter
m	particle mass
beta	inverse temperature
dens	density (reduced by sigma^3)
mu	reduced chemical potential
sx	reduced excess entropy (relative to ideal gas at same temperature and density)
P_MC	reduced pressure from TMMC simulations
P_MD	reduced pressure from MD simulations
D	reduced self-diffusion from MD simulations
+/-	95% confidence intervals for data in preceding column

 

Data:

 

dens	mu	sx	P_MC	P_MD	+/-	D	+/-
0.025	-3.581518	-0.051239	0.026352	0.026346	0.000000	8.338323	0.013053
0.050	-2.775580	-0.106267	0.055593	0.055582	0.000000	4.064806	0.006030
0.075	-2.251420	-0.163217	0.088023	0.088005	0.000002	2.640503	0.002924
0.100	-1.838804	-0.222135	0.123969	0.123942	0.000001	1.934599	0.003292
0.125	-1.483998	-0.283146	0.163795	0.163756	0.000002	1.513458	0.003706
0.150	-1.163011	-0.346350	0.207877	0.207845	0.000003	1.232659	0.002354
0.175	-0.862397	-0.411857	0.256694	0.256646	0.000004	1.033016	0.002243
0.200	-0.574198	-0.479805	0.310713	0.310649	0.000006	0.885175	0.001139
0.225	-0.292855	-0.550336	0.370487	0.370398	0.000006	0.770423	0.000901
0.250	-0.014585	-0.623575	0.436574	0.436478	0.000007	0.679425	0.000883
0.275	0.263858	-0.699679	0.509668	0.509553	0.000010	0.603851	0.001265
0.300	0.544764	-0.778802	0.590437	0.590354	0.000007	0.541249	0.000667
0.325	0.830785	-0.861131	0.679829	0.679687	0.000013	0.487871	0.000904
0.350	1.123470	-0.946850	0.778627	0.778477	0.000013	0.441960	0.000725
0.375	1.424630	-1.036160	0.887818	0.887679	0.000020	0.401539	0.000660
0.400	1.736449	-1.129286	1.008671	1.008452	0.000024	0.365541	0.000291
0.425	2.060345	-1.226464	1.142305	1.142062	0.000021	0.333621	0.000941
0.450	2.398216	-1.327947	1.290155	1.289858	0.000031	0.304674	0.000569
0.475	2.751827	-1.434012	1.453735	1.453388	0.000022	0.278082	0.000337
0.500	3.122964	-1.544949	1.634702	1.634467	0.000025	0.253873	0.000257
0.525	3.514262	-1.661079	1.835287	1.834980	0.000039	0.231995	0.000359
0.550	3.927635	-1.782768	2.057522	2.057119	0.000046	0.211271	0.000357
0.575	4.364901	-1.910388	2.303534	2.303448	0.000018	0.192091	0.000523
0.600	4.829816	-2.044331	2.576735	2.576640	0.000031	0.174733	0.000458
0.625	5.324387	-2.185097	2.879714	2.879972	0.000043	0.157914	0.000271
0.650	5.853256	-2.333129	3.216951	3.216875	0.000067	0.142569	0.000238
0.675	6.415393	-2.488999	3.589434	3.591527	0.000046	0.128386	0.000154
0.700	7.021445	-2.653314	4.006137	4.008462	0.000054	0.114739	0.000185
0.725	7.676348	-2.826629	4.472914	4.472877	0.000055	0.102400	0.000191
0.750	8.387102	-3.010079	4.997208	4.990787	0.000025	0.090396	0.000136
0.775	9.139130	-3.204061	5.570849	5.569115	0.000090	0.079376	0.000099
0.800	9.951519	-3.409416	6.210771	6.215551	0.000097	0.068904	0.000098
0.825	10.849336	-3.627195	6.940487	6.939064	0.000099	0.059316	0.000062
0.850	11.822939	-3.859202	7.755800	7.750263	0.000096	0.050306	0.000035
0.875	12.868237	-4.105596	8.657578	8.661019	0.000063	0.041938	0.000062
0.900	14.019667	-4.367802	9.679868	9.685615	0.000120	0.034327	0.000087

 

Slit Pore Properties

 

 

 

 

 

Figure 1: Schematic of slit-pore geometry. Wall separation is given by H, and center accessible separation given by h=H-sigma, where sigma is the particle diameter.

Data:

H	Wall separation
sx_1	Excess entropy relative to an ideal gas with a  density profile equivalent to the actual fluid
sx_2	Excess entropy relative to an ideal gas with a  uniform density profile
P_MC_T	Pore averaged transverse pressure calculated from TMMC  simulations [3]
P_MD_T	Pore averaged transverse pressure calculated  from molecular dynamics simulations (see  [4])
P_MD_N	Normal pressure calculated from MD simulations
P_bulk_mu	Equilibrium pressure of the bulk fluid (that  is, the pressure of the bulk fluid at the same value of chemical potential)

Note: NaN implies no data available at that state point.

 

 

 

Gap	dens	mu	sx_1	sx_2	P_MC_T	P_MD_T	+/-	P_MD_N	+/-	D	+/-
5.0	0.05	-2.523062	-0.119700	-0.120403	0.070428	0.070431	0.000001	0.069591	0.000001	3.610898	0.007756
5.0	0.10	-1.553323	-0.248980	-0.251914	0.159004	0.159009	0.000002	0.155314	0.000003	1.753338	0.004868
5.0	0.15	-0.840555	-0.386410	-0.392980	0.269691	0.269691	0.000004	0.260541	0.000008	1.141261	0.002083
5.0	0.20	-0.210475	-0.532890	-0.544659	0.407286	0.407305	0.000013	0.389342	0.000011	0.834870	0.001844
5.0	0.25	0.395759	-0.689490	-0.708058	0.577755	0.577737	0.000012	0.546707	0.000011	0.647695	0.001386
5.0	0.30	1.007739	-0.857400	-0.884671	0.788214	0.788213	0.000017	0.738646	0.000019	0.521783	0.002015
5.0	0.35	1.645818	-1.037980	-1.075913	1.047615	1.047615	0.000018	0.972547	0.000013	0.427086	0.001786
5.0	0.40	2.326486	-1.232900	-1.283756	1.366941	1.367078	0.000031	1.257604	0.000045	0.353118	0.000642
5.0	0.45	3.066765	-1.443920	-1.510175	1.760569	1.760472	0.000041	1.605749	0.000037	0.292893	0.000731
5.0	0.50	3.880649	-1.673040	-1.757686	2.244242	2.244863	0.000031	2.032641	0.000047	0.242393	0.000643
5.0	0.55	4.787536	-1.921920	-2.029168	2.839891	2.840505	0.000025	2.558410	0.000044	0.198315	0.000530
5.0	0.60	5.803869	-2.191380	-2.327745	3.571009	3.570998	0.000087	3.206249	0.000090	0.161360	0.000294
5.0	0.65	6.946580	-2.482570	-2.656698	4.464488	4.464864	0.000084	3.997596	0.000074	0.128925	0.000389
5.0	0.70	8.248008	-2.797450	-3.019913	5.563606	5.562612	0.000069	4.945632	0.000111	0.100538	0.000249
5.0	0.75	9.762154	-3.140440	-3.423620	6.937112	6.929774	0.000086	6.054381	0.000110	0.075243	0.000242
5.0	0.80	11.549069	-3.523940	-3.875160	8.670022	8.677227	0.000050	7.328106	0.000186	0.053136	0.000215
5.0	0.85	13.741602	-3.963690	-4.386488	10.932307	10.980952	0.000126	8.796609	0.000246	0.034185	0.000193
5.0	0.90	14.389045	NaN	NaN	11.632706	NaN	NaN	NaN	NaN	NaN	NaN
6.0	0.05	-2.568841	-0.117344	-0.117599	0.067465	0.067459	0.000001	0.066836	0.000002	3.682524	0.007993
6.0	0.10	-1.604890	-0.244385	-0.246502	0.151978	0.151978	0.000004	0.149227	0.000003	1.778212	0.003673
6.0	0.15	-0.898488	-0.379640	-0.384710	0.257277	0.257272	0.000005	0.250429	0.000005	1.151070	0.002664
6.0	0.20	-0.275511	-0.523986	-0.533262	0.387872	0.387877	0.000008	0.374401	0.000005	0.838072	0.002677
6.0	0.25	0.322632	-0.678540	-0.693338	0.549337	0.549312	0.000014	0.525959	0.000013	0.649536	0.001188
6.0	0.30	0.925286	-0.844455	-0.866247	0.748289	0.748349	0.000012	0.710990	0.000012	0.522184	0.000409
6.0	0.35	1.553131	-1.023098	-1.053504	0.993313	0.993324	0.000015	0.936694	0.000016	0.427201	0.000716
6.0	0.40	2.222081	-1.216020	-1.256905	1.294582	1.294602	0.000031	1.211977	0.000027	0.352609	0.000968
6.0	0.45	2.947651	-1.424940	-1.478443	1.664952	1.665002	0.000026	1.547889	0.000060	0.293025	0.000418
6.0	0.50	3.746670	-1.651940	-1.720599	2.120819	2.120647	0.000066	1.958587	0.000050	0.242476	0.000884
6.0	0.55	4.635354	-1.899227	-1.986161	2.681191	2.681461	0.000057	2.462137	0.000028	0.199669	0.000649
6.0	0.60	5.633863	-2.168980	-2.278240	3.370760	3.371777	0.000097	3.081307	0.000071	0.162678	0.000824
6.0	0.65	6.767947	-2.463380	-2.600943	4.222075	4.221458	0.000048	3.841814	0.000077	0.130251	0.000312
6.0	0.70	8.059413	-2.784407	-2.958180	5.269135	5.269621	0.000077	4.768928	0.000091	0.101980	0.000262
6.0	0.75	9.559559	-3.136967	-3.355418	6.575715	6.574329	0.000096	5.886106	0.000108	0.077113	0.000336
6.0	0.80	11.330729	-3.530512	-3.800528	8.224443	8.227210	0.000123	7.226547	0.000163	0.055667	0.000154
6.0	0.85	13.500937	-3.981122	-4.304579	10.375289	10.365951	0.000130	8.876845	0.000432	0.037010	0.000108
6.0	0.90	16.505228	-4.504592	NaN	13.642548	NaN	NaN	NaN	NaN	NaN	NaN
7.0	0.05	-2.600641	-0.115640	-0.115939	0.065478	0.065479	0.000001	0.064986	0.000001	3.729969	0.011858
7.0	0.10	-1.640697	-0.241170	-0.242925	0.147292	0.147295	0.000001	0.145114	0.000004	1.796364	0.003717
7.0	0.15	-0.938752	-0.374691	-0.379067	0.249013	0.249004	0.000004	0.243568	0.000005	1.160307	0.001509
7.0	0.20	-0.320857	-0.517648	-0.525380	0.374943	0.374942	0.000006	0.364213	0.000010	0.842751	0.001596
7.0	0.25	0.271487	-0.670559	-0.683001	0.530397	0.530389	0.000018	0.511760	0.000018	0.650426	0.001899
7.0	0.30	0.868022	-0.835136	-0.853305	0.721861	0.721848	0.000013	0.691981	0.000026	0.520877	0.001007
7.0	0.35	1.488327	-1.012263	-1.037794	0.957212	0.957270	0.000013	0.911912	0.000025	0.427374	0.000729
7.0	0.40	2.149188	-1.203859	-1.238073	1.246569	1.246517	0.000043	1.180310	0.000042	0.352527	0.001370
7.0	0.45	2.864824	-1.411375	-1.456240	1.601708	1.601907	0.000029	1.507977	0.000034	0.292858	0.000549
7.0	0.50	3.652093	-1.637099	-1.694615	2.038370	2.038643	0.000032	1.908438	0.000043	0.243090	0.000211
7.0	0.55	4.529029	-1.883148	-1.956063	2.575975	2.576109	0.000057	2.398874	0.000052	0.200323	0.000245
7.0	0.60	5.513861	-2.152178	-2.243575	3.237230	3.238169	0.000096	3.000984	0.000073	0.163185	0.000391
7.0	0.65	6.632302	-2.446995	-2.561300	4.053477	4.054812	0.000048	3.741582	0.000063	0.131379	0.000405
7.0	0.70	7.912163	-2.769997	-2.913233	5.062123	5.064299	0.000067	4.651018	0.000099	0.103401	0.000315
7.0	0.75	9.391189	-3.127170	-3.305240	6.314396	6.319617	0.000074	5.763342	0.000131	0.078844	0.000277
7.0	0.80	11.149337	-3.523552	-3.744325	7.905501	7.897676	0.000121	7.126259	0.000161	0.057480	0.000170
7.0	0.85	13.224048	-3.972839	-4.240474	9.904432	9.901127	0.000192	8.840516	0.000239	0.039114	0.000097
7.0	0.90	15.630033	-4.476738	NaN	12.361201	NaN	NaN	NaN	NaN	NaN	NaN
7.5	0.05	NaN	NaN	NaN	NaN	0.064716	0.000001	0.064272	0.000001	3.749998	0.007295
7.5	0.10	NaN	NaN	NaN	NaN	0.145493	0.000004	0.143522	0.000004	1.804281	0.004415
7.5	0.15	NaN	NaN	NaN	NaN	0.245823	0.000006	0.240898	0.000005	1.161573	0.001582
7.5	0.20	NaN	NaN	NaN	NaN	0.369979	0.000006	0.360250	0.000006	0.844042	0.001627
7.5	0.25	NaN	NaN	NaN	NaN	0.523128	0.000013	0.506226	0.000010	0.652081	0.001642
7.5	0.30	NaN	NaN	NaN	NaN	0.711673	0.000020	0.684551	0.000017	0.522322	0.001894
7.5	0.35	NaN	NaN	NaN	NaN	0.943429	0.000028	0.902224	0.000035	0.427207	0.001074
7.5	0.40	NaN	NaN	NaN	NaN	1.228091	0.000032	1.167894	0.000048	0.353778	0.001053
7.5	0.45	NaN	NaN	NaN	NaN	1.577673	0.000038	1.492294	0.000029	0.293238	0.000931
7.5	0.50	NaN	NaN	NaN	NaN	2.007224	0.000022	1.888848	0.000059	0.243392	0.000585
7.5	0.55	NaN	NaN	NaN	NaN	2.535604	0.000075	2.374142	0.000063	0.200860	0.000535
7.5	0.60	NaN	NaN	NaN	NaN	3.186788	0.000093	2.969176	0.000075	0.164173	0.000511
7.5	0.65	NaN	NaN	NaN	NaN	3.991370	0.000096	3.700630	0.000094	0.131882	0.000266
7.5	0.70	NaN	NaN	NaN	NaN	4.988454	0.000075	4.605141	0.000119	0.104081	0.000171
7.5	0.75	NaN	NaN	NaN	NaN	6.224015	0.000092	5.731521	0.000089	0.079456	0.000155
7.5	0.80	NaN	NaN	NaN	NaN	7.749119	0.000062	7.135838	0.000124	0.058210	0.000159
7.5	0.85	NaN	NaN	NaN	NaN	9.622471	0.000150	8.848316	0.000234	0.039923	0.000186
8.0	0.05	-2.624020	-0.114500	-0.114905	0.064061	0.064064	0.000001	0.063658	0.000000	3.770250	0.006176
8.0	0.10	-1.666879	-0.238670	-0.240384	0.143965	0.143952	0.000002	0.142151	0.000002	1.812298	0.002364
8.0	0.15	-0.968441	-0.371160	-0.374984	0.243109	0.243107	0.000002	0.238610	0.000008	1.166124	0.002646
8.0	0.20	-0.354264	-0.512830	-0.519630	0.365721	0.365719	0.000007	0.356830	0.000008	0.845826	0.001143
8.0	0.25	0.233732	-0.664730	-0.675495	0.516880	0.516907	0.000008	0.501450	0.000016	0.651550	0.001909
8.0	0.30	0.825575	-0.828070	-0.843801	0.702955	0.702954	0.000012	0.678140	0.000023	0.523422	0.001404
8.0	0.35	1.440646	-1.004180	-1.026054	0.931564	0.931554	0.000023	0.893824	0.000031	0.427972	0.000715
8.0	0.40	2.095303	-1.194660	-1.224117	1.212357	1.212268	0.000017	1.157127	0.000029	0.353869	0.000868
8.0	0.45	2.804028	-1.401210	-1.439753	1.556898	1.556956	0.000036	1.478688	0.000024	0.293908	0.000649
8.0	0.50	3.583470	-1.625860	-1.675363	1.980404	1.980399	0.000051	1.871762	0.000048	0.243357	0.000803
8.0	0.55	4.450287	-1.871010	-1.933741	2.500947	2.501251	0.000047	2.353129	0.000059	0.201529	0.000339
8.0	0.60	5.425181	-2.139340	-2.217999	3.142140	3.142835	0.000070	2.943826	0.000111	0.164520	0.000314
8.0	0.65	6.531029	-2.433780	-2.531823	3.932751	3.934696	0.000044	3.670595	0.000108	0.132660	0.000258
8.0	0.70	7.804626	-2.758190	-2.880261	4.916097	4.914320	0.000062	4.565729	0.000112	0.104754	0.000187
8.0	0.75	9.269163	-3.116060	-3.268262	6.130574	6.131574	0.000106	5.667944	0.000109	0.080081	0.000204
8.0	0.80	10.987243	-3.513730	-3.702052	7.653868	7.654425	0.000155	7.030824	0.000082	0.058794	0.000219
8.0	0.85	13.000985	-3.959060	-4.191299	9.553840	9.565989	0.000169	8.748016	0.000313	0.040538	0.000121
8.0	0.90	15.385838	-4.447830	NaN	11.940553	NaN	NaN	NaN	NaN	NaN	NaN
9.0	0.05	-2.641729	-0.113442	-0.113423	0.063006	0.063003	0.000001	0.062658	0.000001	3.800816	0.006367
9.0	0.10	-1.687112	-0.236785	-0.237875	0.141449	0.141444	0.000004	0.139914	0.000003	1.823410	0.003640
9.0	0.15	-0.991100	-0.368236	-0.371362	0.238700	0.238684	0.000003	0.234857	0.000007	1.172099	0.002518
9.0	0.20	-0.379936	-0.509107	-0.514776	0.358804	0.358804	0.000008	0.351236	0.000009	0.848748	0.002412
9.0	0.25	0.205031	-0.660059	-0.669248	0.506834	0.506806	0.000007	0.493621	0.000015	0.654682	0.002184
9.0	0.30	0.793081	-0.822592	-0.836132	0.688830	0.688800	0.000010	0.667606	0.000029	0.524030	0.000874
9.0	0.35	1.403831	-0.997799	-1.016817	0.912281	0.912319	0.000023	0.880052	0.000033	0.428553	0.000666
9.0	0.40	2.053439	-1.187455	-1.213037	1.186552	1.186646	0.000013	1.139461	0.000038	0.354097	0.000679
9.0	0.45	2.757311	-1.393174	-1.426736	1.523381	1.523347	0.000021	1.456305	0.000035	0.294409	0.000642
9.0	0.50	3.530144	-1.617063	-1.660279	1.936732	1.936880	0.000028	1.843732	0.000028	0.244614	0.000428
9.0	0.55	4.390853	-1.861504	-1.916330	2.445541	2.445263	0.000046	2.318197	0.000064	0.202047	0.000255
9.0	0.60	5.358016	-2.129296	-2.198093	3.071731	3.071491	0.000060	2.900525	0.000064	0.165315	0.000403
9.0	0.65	6.454986	-2.423515	-2.509107	3.843736	3.844430	0.000070	3.616991	0.000057	0.133591	0.000196
9.0	0.70	7.712832	-2.747473	-2.854180	4.799765	4.800968	0.000112	4.500636	0.000043	0.105709	0.000255
9.0	0.75	9.168933	-3.106304	-3.238723	5.988516	5.988933	0.000111	5.592164	0.000123	0.081220	0.000180
9.0	0.80	10.874549	-3.503939	-3.668175	7.477441	7.471133	0.000067	6.946346	0.000108	0.060102	0.000165
9.0	0.85	12.862319	-3.946623	-4.151619	9.324232	9.323168	0.000057	8.647043	0.000262	0.041693	0.000096
9.0	0.90	15.158590	-4.429011	NaN	11.585506	NaN	NaN	NaN	NaN	NaN	NaN
10.0	0.05	-2.655929	-0.112760	-0.113116	0.062175	0.062179	0.000001	0.061880	0.000001	3.828065	0.008916
10.0	0.10	-1.702996	-0.235300	-0.236657	0.139501	0.139498	0.000003	0.138168	0.000003	1.834671	0.004733
10.0	0.15	-1.009155	-0.366100	-0.369087	0.235254	0.235248	0.000004	0.231917	0.000008	1.177262	0.003609
10.0	0.20	-0.400188	-0.506140	-0.511435	0.353445	0.353438	0.000005	0.346848	0.000005	0.850134	0.002086
10.0	0.25	0.182100	-0.656430	-0.664817	0.498973	0.498963	0.000018	0.487474	0.000013	0.655563	0.001497
10.0	0.30	0.767246	-0.818180	-0.830457	0.677832	0.677806	0.000018	0.659342	0.000012	0.525334	0.000744
10.0	0.35	1.374626	-0.992750	-1.009819	0.897308	0.897357	0.000017	0.869223	0.000017	0.429175	0.000592
10.0	0.40	2.020643	-1.181660	-1.204601	1.166692	1.166719	0.000023	1.125537	0.000027	0.354984	0.000341
10.0	0.45	2.720036	-1.386730	-1.416804	1.497243	1.497264	0.000022	1.438690	0.000048	0.295404	0.000475
10.0	0.50	3.488151	-1.609940	-1.648616	1.903006	1.903022	0.000038	1.821591	0.000059	0.245625	0.000558
10.0	0.55	4.342587	-1.853810	-1.902708	2.401861	2.401853	0.000031	2.290708	0.000056	0.203296	0.000567
10.0	0.60	5.302675	-2.120990	-2.182286	3.015806	3.016096	0.000075	2.866433	0.000077	0.166396	0.000239
10.0	0.65	6.392146	-2.414780	-2.491118	3.773039	3.774290	0.000033	3.574953	0.000038	0.134562	0.000186
10.0	0.70	7.641344	-2.738850	-2.833660	4.710694	4.712470	0.000111	4.449126	0.000082	0.106676	0.000187
10.0	0.75	9.079698	-3.097300	-3.214587	5.870472	5.877442	0.000077	5.530702	0.000063	0.082347	0.000143
10.0	0.80	10.760901	-3.495590	-3.641881	7.318974	7.329399	0.000067	6.874078	0.000147	0.060909	0.000141
10.0	0.85	12.736051	-3.938110	-4.122407	9.130506	9.141104	0.000117	8.556013	0.000213	0.042495	0.000074
10.0	0.90	15.013105	-4.421070	NaN	11.344811	NaN	NaN	NaN	NaN	NaN	NaN
15.0	0.05	-2.697185	-0.110414	-0.110458	0.059822	0.059824	0.000001	0.059645	0.000001	3.899576	0.005454
15.0	0.10	-1.749725	-0.230747	-0.231439	0.133945	0.133940	0.000002	0.133141	0.000004	1.864668	0.003974
15.0	0.15	-1.061974	-0.359472	-0.361170	0.225453	0.225452	0.000003	0.223446	0.000003	1.192309	0.002397
15.0	0.20	-0.459774	-0.497250	-0.500528	0.338152	0.338132	0.000006	0.334154	0.000006	0.861787	0.001197
15.0	0.25	0.114696	-0.645286	-0.650663	0.476595	0.476597	0.000010	0.469637	0.000013	0.663227	0.000896
15.0	0.30	0.691041	-0.804982	-0.812776	0.646467	0.646493	0.000006	0.635275	0.000014	0.530581	0.000762
15.0	0.35	1.288918	-0.977541	-0.988319	0.854786	0.854773	0.000015	0.837655	0.000026	0.433637	0.000593
15.0	0.40	1.923592	-1.164250	-1.178963	1.109986	1.110019	0.000026	1.084896	0.000029	0.359106	0.000945
15.0	0.45	2.609898	-1.367111	-1.386525	1.422756	1.422911	0.000035	1.387178	0.000026	0.299288	0.000430
15.0	0.50	3.363557	-1.588511	-1.613317	1.806653	1.806744	0.000046	1.756972	0.000040	0.249353	0.000550
15.0	0.55	4.200814	-1.830632	-1.861848	2.278025	2.278204	0.000030	2.210155	0.000048	0.206959	0.000337
15.0	0.60	5.141221	-2.095960	-2.135357	2.857884	2.858447	0.000022	2.766619	0.000073	0.170705	0.000615
15.0	0.65	6.209108	-2.388056	-2.437320	3.573661	3.574262	0.000062	3.451758	0.000077	0.138541	0.000317
15.0	0.70	7.431799	-2.711255	-2.772134	4.458694	4.460000	0.000035	4.297887	0.000097	0.110500	0.000360
15.0	0.75	8.839178	-3.070076	-3.145232	5.552641	5.559524	0.000062	5.346428	0.000098	0.086070	0.000297
15.0	0.80	10.484866	-3.469050	-3.563044	6.920035	6.929339	0.000096	6.650362	0.000156	0.064573	0.000276
15.0	0.85	12.432600	-3.912918	-4.032293	8.643062	8.641765	0.000102	8.278002	0.000083	0.045855	0.000036
15.0	0.90	14.681943	-4.408871	NaN	10.752998	NaN	NaN	NaN	NaN	NaN	NaN

Self-diffusion versus density	Self-diffusion vs excess entropy type 1
Self-diffusion vs excess entropy type 2

 

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