V. I. Shmotolokha ∗,M. F. HolovkoInstitute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii St.,79011 Lviv, UkraineReceived November 21, 2023This research focuses on the unique phase behavior of non-spherical patchy colloids in porous environments. Based on the theory of scaled particle (SPT), methods have been refined and applied to analyze the thermodynamic properties of non-spherical patchy particles in a disordered porous medium. Utilizing the associative theory of liquids in conjunction with SPT, we investigated the impact of associative interactions and connections between the functional nodes of particles on the formation of the nematic phase. Calculations of orientational and spatial distributions were conducted, which helped to understand the phase behavior of particles during the transition from isotropic to nematic phase under the spatial constraints imposed by the disordered matrix of the porous medium.Keywords: patchy colloids, spherocylinders, dimerization, disordered porous media, geometrical porosity,probe particle porosity
1 at infinite dilution. 13607-6 Dimerizing hard spherocylinders in porous media In this case we are considering = (1 0) exp (cid:26) 0 1 0 (cid:20) 3 2 (1 + 1) + 31 (cid:21) 2 0 (1 0)2 1 2 9 2 0 (1 0)3 12 (31 1)3(1 + 0 + 2 0) (cid:27) , where = 1 0 , 1 = 1 + 1 1 . For the free energy, we can get an expression from the thermodynamic relationship = 1 1 . The free energy, limited by fluid in the SPT2b1 approximation, is presented as follows: (cid:18) (cid:19) SPT2b1 1 0 1 1/0 1 1/0 = ( 1, 10) + ln 1 ln(1 1/0) (cid:18) (cid:19) (cid:20) (cid:21) 0 (cid:0)( 1)(cid:1) 2 ln(1 1/0) + 1 1 + (cid:0)( 1)(cid:1) 3 (cid:18) 1/0 1 1/0 + + According to the , we should add the CS terms to expressions (2.8), (2.9), and (2.18). (cid:18) 1 (cid:19) SPT2b1-CS = (cid:18) 1 (cid:19) SPT2b1 + (cid:18) 1 (cid:19) CS , (1)SPT2b1-CS = (1)SPT2b1 + (1)CS , (cid:18) 1 (cid:19) SPT2b1-CS = (cid:18) 1
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(cid:19) SPT2b1 + (cid:18) 1 (cid:19) CS , where (cid:18) 1 (cid:19) CS = (1/0)3 (1 1/0)3 , (1)CS = ln (cid:18) (cid:19) 1 0 (cid:18) 1/0 1 1/0 1 + 1/0 1 1/0 (cid:19) 3 , 1 2 (cid:18) 1/0 1 1/0 (cid:19) 2 (cid:18) 1 (cid:19) CS = ln (cid:18) 1 1 0 (cid:19) + 1/0 1 1/0 1 2 (cid:18) 1/0 1 1/0 (cid:19) 2 . (cid:19) 2 . (2.17) (2.18) (2.19) (2.20) (2.21) (2.22) (2.23) (2.24) (2.25) 13607-7 V. I. Shmotolokha, M. F. Holovko 2.2. Associative contribution and the integral equations for the singlet distribution
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5), in which the first two terms can be presented in the form (2.19). This expression includes contributions from hard spherocylinders and from associative interactions. To complete this, we should determine the expressions for the singlet distribution functions 1(1) = 1 1(1) and 10(1) = 10 10(1). Both functions can be found from the minimization of the free energy with respect to variations in these distributions. In particular, from variation in 10(1), we have the generalization of a very known relation between 1(1) and 10(1) in the theory of associative fluids for the anisotropic associative fluids in porous media, which plays the role of the mass action law (MAL) in the theory of associative fluids: 1(1) = 10(1) + 10(1) 10(2)HCS(12) as(12) d2. (2.26)
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In this relation, it is convenient, according to (2.3), to move from 1(1) and 10(1) to functions 1(1) and 10(1). Since in the isotropic phase the functions 1(1) = 10(1) = 1 and in the nematic phase all spherocylinders are nearly parallel, in (2.26) we can use the approximation 10(2) = 10(1), for the first time introduced by Sear and Jackson . Finally, due to the delta-like character of the associative interaction, the relation (2.26) can be written in the form: 1(1) = 10(1) + 2 2 10(1) 1 cont HCS , (2.27) where = 10/1 is the fraction of monomers, = exp(1) 1, and is the geometric multiplier, determined by the volume of overlap of the two interactive bonding sites . The contact value of the binary function of hard spherocylinders cont HSC will be approximated by the corresponding contact value of hard spheres, which, with the help of previous works [8, 9], can be presented in the following form:
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